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Uniform Labelled Calculi for Conditional and Counterfactual Logics

Conference paper
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 11541)

Abstract

Lewis’s counterfactual logics are a class of conditional logics that are defined as extensions of classical propositional logic with a two-place modal operator expressing conditionality. Labelled proof systems are proposed here that capture in a modular way Burgess’s preferential conditional logic \( \mathbb {PCL}\), Lewis’s counterfactual logic \( \mathbb {V}\), and their extensions. The calculi are based on preferential models, a uniform semantics for conditional logics introduced by Lewis. The calculi are analytic, and their completeness is proved by means of countermodel construction. Due to termination in root-first proof search, the calculi also provide a decision procedure for the logics.

Keywords

Conditional logics Counterfactual logics Proof theory Preferential models Labelled calculi 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Aix Marseille Univ, Université de Toulon, CNRS, LISMarseilleFrance
  2. 2.University of HelsinkiHelsinkiFinland
  3. 3.The Ohio State UniversityColumbusUSA

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